在現今，產品大多具備高可靠度的性質，生產者為了要提升產品競爭力，需要不斷地提供顧客關於可靠度的資訊，如產品的壽命推論，而衰變試驗(degradation test) 常被用來推估壽命相關資訊。因此，如何建構衰變模型及推論產品壽命分配，將是我們所要解決的問題。關於衰變模型之建構，文獻上大多以隨機效應模型、 Wiener、Gamma、Inverse Gaussian 過程之衰變模型來描述，而這些模型皆有各自對應之壽命分配。然而針對 Tweedie 衰變模型，其壽命分配沒有解析解。因此，本研究將利用 Inverse Laplace Transformation、Saddlepoint Approximation 及 Birnbaum-Saunders 分配近似這三種方式對 Tweedie 衰變模型計算產品壽命的分配進而推估產品壽命，本研究亦將衰變模型加上隨機效應項進行分析。第二部份重點為如何選擇適合的模型去配適衰變資料，選模是利用 Akaike information criterion (AIC) 和對壽命資訊做適合度檢定這兩個準則來挑選。本文也將拿 Gamma 、 Inverse Gaussian 與 Tweedie 衰變模型做比較，並帶入三個實際例子去看哪種模型較適合衰變資料。最後透過模擬研究可發現，在同時使用 AIC 及壽命分配之適合度檢定為準則下，有較高的比例挑選到正確的模型。

Degradation models are widely used to assess the lifetime information of highly reliable products with quality characteristics. The purpose of this study is divided into two parts, the first part will use Inverse Laplace Transformation, Saddlepoint Approximation and Birnbaum-Saunders distribution approximation to calculate the product's lifetime distribution based on Tweedie degradation model, and this study also analyze the degradation model with the random effect model. The second part focuses how to choose the appropriate model to match the degradation data, by using the Akaike information criterion (AIC) and the goodness-of-fit for lifetime information together. This study will also compare Gamma, Inverse Gaussian degradation model with the Tweedie degradation model on three practical degradation examples, and the results will show which models are more suitable for the degradation examples.

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